A crown gear is a gear whose teeth project axially from the face of a flat disc, like the crown of a king turned sideways. It meshes with a standard spur pinion whose axis is perpendicular to the crown's axis, producing a 90° direction change without the complex tooth geometry of bevel gears. Think of it as the poor man's bevel gear: cheaper to make, more forgiving of misalignment, but limited to lighter loads.

Crown gears differ from bevel gears in one key way: the pinion is a plain cylindrical spur gear, not a conical bevel pinion. This means the pinion can slide axially along its shaft without losing engagement — a property exploited in differential mechanisms in vintage clocks and early mechanical calculators (Pascal's Pascaline used crown-gear-like teeth for its carry mechanism). The pinion contacts only a small arc of the crown's teeth, so load capacity is modest.

Where you actually see them today:

• Hand drills and eggbeater drills — the crank turns a large crown gear that drives a small spur pinion on the chuck shaft, giving both 90° redirection and a step-up ratio
• Music boxes — the wound spring drives a governor through a crown-and-pinion pair
• Kitchen mixers and eggbeaters — a single crown gear drives two counter-rotating pinions for the beaters
• Toys and low-cost gearboxes where noise and precision don't matter

The geometry rule of thumb: the gear ratio is simply the tooth count ratio, same as any gear pair. For a crown with 60 teeth driving a pinion with 12 teeth, ratio = 60/12 = 5:1 reduction (or 5:1 step-up if you drive the pinion). The pitch diameter of the crown at the tooth contact circle equals N × module, exactly like a spur gear laid flat.

Why they've mostly disappeared from serious machinery: tooth contact is essentially point contact rather than the line contact of proper bevel gears, so contact stresses are high and wear is fast under load. They also can't handle high speeds — the pinion's cylindrical teeth don't roll smoothly against the crown's radially-arrayed teeth, causing sliding, noise, and heat. For any application above a few Nm of torque or a few hundred RPM, engineers reach for bevel gears instead.

Design tip: position the pinion so it contacts the crown at roughly 2/3 of the crown's radius from center — closer in and the teeth converge too much; farther out and you waste material. Backlash is set by the axial position of the pinion, which is why hand drills often feel gritty after decades of wear.